Ace Your Binomial Probability Tests with Plainmath's Expert Help and Detailed Resources

It is conjectured that an impurity exists in 30% of all drinking wells in a certain rural community. In order to gain some insight on this problem, it is determined that some tests should be made. It is too expensive to test all of the many wells in the area, so 10 were randomly selected for testing. a. Using the binomial distribution, what is the probability that exactly three wells have the impurity assuming that the conjecture is correct? b. What is the probability that more than three wells are impure?

Customers at a gas station pay with a credit card (A), debit card (B), or cash (C). Assume that successive customers make independent choices with ${\displaystyle P\left(A\right)=0.4,P\left(B\right)=0.2,\text{and}P\left(C\right)=0.4}$.
(a) Among the next 100 customers, what are the mean and variance of the number who pay with a debit card?
$$\begin{array}{|cc|}\hline mean& customers\\ variance& customer{s}^2\\ \hline\end{array}$$
Explain your reasoning.
Because we are interested in whether or not a debit card was used, we can use the binomial distribution. ${\displaystyle X=}$ the probability that a customer used a debit card.Because we are interested in whether or not a debit card was used, we can use the binomial distribution. ${\displaystyle X=}$ the number of customers who use a debit card. Because we are interested in whether or not a debit card was used, we can use the binomial distribution. ${\displaystyle X=}$ the number of customers at the gas station.
(b) Answer part (a) for the number among the 100 who dont

a) Market research has shown that 60% of persons who are introduced to a certain product actually buy the product. A random sample of 15 persons were introduced to the product.
i. Define the variable of interest for this scenario.
ii. What probability distribution do you think best describes the situation? Why?
iii. Calculate the probability that exactly 9 will buy the product.

An oil drilling company ventures into various locations, and its success or failure is independent from one location to another. Suppose the probability of a success at any specific location is 0.30. What is the probability that a driller drills 10 locations and finds 1 success? The driller feels that he will go bankrupt if he drills 10 times before the first success occurs. What are the driller's prospects for bankruptcy? i. ii.

What does exclamation an point mean?

Tell, what is the factorial of 10?

Beth is taking an eleven​-question ​multiple-choice test for which each question has three answer​ choices, only one of which is correct. Beth decides on answers by rolling a fair die and marking the first answer choice if the die shows 1 or​ 2, the second if the die shows 3 or​ 4, and the third if the die shows 5 or 6. Find the probability of the stated event.
exactly
four
correct answers

The Hawkins Company randomly samples 10 items from every large batch before the batch is packaged and shipped. According to the contract specifications, 5 percent of the items shipped can be defective. If the inspectors find 1 or fewer defects in the sample of 10, they ship the batch without further inspection. If they find 2 or more, the entire batch is inspected.
If they find 2 or more, the entire batch is inspected. Based on this sampling plan, the probability that a batch that meets the contract requirements will end up being 100 percent inspected is approximately...
A) .086
B) .41
C) .68
D) There is insufficient information to answer

In a 10-question true/false test, what is the probability of guessing correctly on questions 1 through 4 exactly 2 times?

The probability that a student passes the Probability and Statistics exam is 0.7.
(i)Find the probability that a given student will pass the Probability and Statistics exam after the third try.
(ii)Find the probability that the third student who fails the Probability and Statistics exam is found after the fifth student in a class of 9 students?
(iii)Find the probability that at most 3 students will pass the Probability and Statistics exam in a class of 7 students.

An insurance company found that 25% of all insurance policies are terminated before their maturity date. Assume that 10 polices are randomly selected from the company’s policy database. Assume a Binomial experiment.
Required:
What is the probability that at most eight policies are not terminated before maturity?

Consider a binomial experiment with ${\displaystyle n=20\text{and}p=.70}$.
1. Compute f (12).
2. Compute f (16).
3. Compute ${\displaystyle P(x\ge 16)}$.

Suppose we have two weighted coins, one of which comes up heads with probability 0.3, and the other of which comes up heads with probability 0.8. Unfortunately, the coins are otherwise identical, and we have lost track of which is which. Suppose we flip a randomly chosen coin 14 times and let N be the random variable giving the number of heads seen. If in the first 3 flips we see 2 heads, what is the conditional expected number of heads in the 14 flips?
${\displaystyle E\left[N\mid 2\text{of first 3 are H}\right]=?}$

Imagine that the probability that a random person will receive a phone call during this exam is approximately 16%. Let's assume that there are 24 students taking this exam. What is the probability that at least one student will receive a phone call during the exam?

When Tim Hortons used physical cups for their Roll up the Rim contest (before switching over to "digital cups") they printed the cups so that 1 out of every 6 cups would be a winner. If the winning cups are truly randomly spread throughout the country.
a) A person feels they are particularly unlucky when it came to buying Tim Hortons coffee and winning Roll up the Rim. They often tell the story about how they kept buying losing coffee cups until the 16th cup was their first winning cup. What is the probability that someone could purchase this many cups and only win on the 16th cup?

A batch of 400 LEDS contains 7 that are defective. This is known to be the long-term average for the production. The company sells boxes with 50 LEDS in each box.
(a) What is the probability there are 1 or more defective bulbs in a box?
(b) If three LEDS are selected at random from a box, what is the probability that the third one selected is defective given that the first one selected was not defective and the second one selected was defective?
(c) Boxes are returned if 3 or more are defective. What is the probably a box will be returned?

A component may come from any one of three manufacturers with probabilities ${\displaystyle p1=0.25,p2=0.50,\text{and}p3=0.25}$. The probabilities that the components will function properly are a function of the manufacturer and are 0.1, 0.2, and 0.4 for the first, second, and third manufacturer, respectively.
a. Compute the probability that a randomly chosen component will function properly.
b. Compute the probability that three components in series randomly selected will function properly

In an assembly of 200 people there approximately 2% of them are civil engineers. If we randomly select five people, what is the probability of them being civil engineers?